Install the System Prerequisites

yum install mysql-server httpd nano php php-mysql
chkconfig httpd on
chkconfig mysqld on
service mysqld start
service httpd start

Create the Database

mysqladmin create wordpress
mysql
mysql> GRANT ALL PRIVILEGES ON wordpress.* TO 'wordpress'@'localhost' IDENTIFIED BY 'please+use+a+strong+password';
mysql> FLUSH PRIVILEGES;
mysql> quit

Download and Install WordPress

cd /var/www/
mkdir wordpress
cd wordpress
curl -O http://wordpress.org/latest.tar.gz
tar xvfz latest.tar.gz
rm latest.tar.gz
mv wordpress/ public
mkdir logs public/wp-content/uploads public/wp-content/cache
chown apache:apache logs public/wp-content/uploads public/wp-content/cache
cd public/

Configure WordPress

Create the WordPress config file outside web root:

mv wp-config-sample.php ../wp-config.php
curl https://api.wordpress.org/secret-key/1.1/salt/

Copy the output to your clipboard before editing wp-config.php.

nano ../wp-config.php
define('DB_NAME', 'wordpress');
define('DB_USER', 'wordpress');
define('DB_PASSWORD', 'enter+the+strong+password+you+defined');
define('DB_HOST', 'localhost');

define('AUTH_KEY', 'pasted from clipboard');
define('SECURE_AUTH_KEY', 'pasted from clipboard');
define('LOGGED_IN_KEY', 'pasted from clipboard');
define('NONCE_KEY', 'pasted from clipboard');
define('AUTH_SALT', 'pasted from clipboard');
define('SECURE_AUTH_SALT', 'pasted from clipboard');
define('LOGGED_IN_SALT', 'pasted from clipboard');
define('NONCE_SALT', 'pasted from clipboard');

Configure Apache

nano /etc/httpd/conf.d/wordpress.conf
NameVirtualHost *:80
<VirtualHost *:80>
	ServerAdmin webmaster@dummy-host.example.com
	DocumentRoot /var/www/wordpress/public
	ServerName dummy-host.example.com
	ErrorLog /var/www/wordpress/logs/error_log
	CustomLog /var/www/wordpress/logs/access_log common
	<Directory /var/www/wordpress/public/wp-content>
		Options FollowSymLinks # for pretty permalink support
		RemoveHandler .php
		RemoveType text/html .php
service httpd restart

Acknowledgements

How to Install WordPress on CentOS 5 in Five Minutes Flat. Cutler, Andrew. Adlibre. 2010.